{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:P3WRFVLYUYLMSIIZE5K2CUUUJN","short_pith_number":"pith:P3WRFVLY","canonical_record":{"source":{"id":"1809.00932","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-04T13:07:52Z","cross_cats_sorted":["cs.DS","cs.LG"],"title_canon_sha256":"96e193e0dd28a1e729ae86d216fb77cd39fbff4fd4c3dfa7872ebeffe3dc8bdb","abstract_canon_sha256":"7934751a7d7d3a7fbc1c19e4224301233e9c0ea2c0e4c1b0a6c2dde53e69002d"},"schema_version":"1.0"},"canonical_sha256":"7eed12d578a616c921192755a152944b5a964289938cf5a2e9c188bc250bee84","source":{"kind":"arxiv","id":"1809.00932","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00932","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00932v2","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00932","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"P3WRFVLYUYLM","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P3WRFVLYUYLMSIIZ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P3WRFVLY","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:P3WRFVLYUYLMSIIZE5K2CUUUJN","target":"record","payload":{"canonical_record":{"source":{"id":"1809.00932","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-04T13:07:52Z","cross_cats_sorted":["cs.DS","cs.LG"],"title_canon_sha256":"96e193e0dd28a1e729ae86d216fb77cd39fbff4fd4c3dfa7872ebeffe3dc8bdb","abstract_canon_sha256":"7934751a7d7d3a7fbc1c19e4224301233e9c0ea2c0e4c1b0a6c2dde53e69002d"},"schema_version":"1.0"},"canonical_sha256":"7eed12d578a616c921192755a152944b5a964289938cf5a2e9c188bc250bee84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:10.981256Z","signature_b64":"QR2n4JJl9LOx82qau7ym9zOIAOBBUCTqbUa9pu9RsBpqY1yzwREp+jx+c7BUKqXbZPCEM3itP7amwEzn4rmZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7eed12d578a616c921192755a152944b5a964289938cf5a2e9c188bc250bee84","last_reissued_at":"2026-05-18T00:06:10.980554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:10.980554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.00932","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ex9FVjaavnwc8AI8CCUituv4Rkbu/zu3N+VYQH2jlA9JfOpQrbatsnkzcKNpdqNI/iLM74lwQqwS3i+xaUSHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T02:21:00.000268Z"},"content_sha256":"4522dabc8b16f0e232a660804a412136fe0eb357420a88dfe6f156e5f36916ce","schema_version":"1.0","event_id":"sha256:4522dabc8b16f0e232a660804a412136fe0eb357420a88dfe6f156e5f36916ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:P3WRFVLYUYLMSIIZE5K2CUUUJN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster Balanced Clusterings in High Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"cs.CG","authors_text":"Hu Ding","submitted_at":"2018-09-04T13:07:52Z","abstract_excerpt":"The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by the given lower and upper bounds. The problems are motivated by the applications in processing large-scale data in high dimension. Existing methods often need to compute complicated matchings (or min cost flows) to satisfy the balance constraint, and thus suffer from high complexities especially in high dimension. We develop an effective framework for the thr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00932","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aBZYa4ljnJW7KXBGXeOPhwXvQnLwl9HHUEY1Pz4MF94ulYC13SjYpCk39ufek8OdkuYyZCVCRLeWA2tBlD3fCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T02:21:00.000640Z"},"content_sha256":"841272cc4d116806a02a97a1be02d0eb1d1f9a092efb5abf653d2b62121069ed","schema_version":"1.0","event_id":"sha256:841272cc4d116806a02a97a1be02d0eb1d1f9a092efb5abf653d2b62121069ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3WRFVLYUYLMSIIZE5K2CUUUJN/bundle.json","state_url":"https://pith.science/pith/P3WRFVLYUYLMSIIZE5K2CUUUJN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3WRFVLYUYLMSIIZE5K2CUUUJN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-04T02:21:00Z","links":{"resolver":"https://pith.science/pith/P3WRFVLYUYLMSIIZE5K2CUUUJN","bundle":"https://pith.science/pith/P3WRFVLYUYLMSIIZE5K2CUUUJN/bundle.json","state":"https://pith.science/pith/P3WRFVLYUYLMSIIZE5K2CUUUJN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3WRFVLYUYLMSIIZE5K2CUUUJN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P3WRFVLYUYLMSIIZE5K2CUUUJN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7934751a7d7d3a7fbc1c19e4224301233e9c0ea2c0e4c1b0a6c2dde53e69002d","cross_cats_sorted":["cs.DS","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-04T13:07:52Z","title_canon_sha256":"96e193e0dd28a1e729ae86d216fb77cd39fbff4fd4c3dfa7872ebeffe3dc8bdb"},"schema_version":"1.0","source":{"id":"1809.00932","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00932","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00932v2","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00932","created_at":"2026-05-18T00:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"P3WRFVLYUYLM","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P3WRFVLYUYLMSIIZ","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P3WRFVLY","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:841272cc4d116806a02a97a1be02d0eb1d1f9a092efb5abf653d2b62121069ed","target":"graph","created_at":"2026-05-18T00:06:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by the given lower and upper bounds. The problems are motivated by the applications in processing large-scale data in high dimension. Existing methods often need to compute complicated matchings (or min cost flows) to satisfy the balance constraint, and thus suffer from high complexities especially in high dimension. We develop an effective framework for the thr","authors_text":"Hu Ding","cross_cats":["cs.DS","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-04T13:07:52Z","title":"Faster Balanced Clusterings in High Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00932","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4522dabc8b16f0e232a660804a412136fe0eb357420a88dfe6f156e5f36916ce","target":"record","created_at":"2026-05-18T00:06:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7934751a7d7d3a7fbc1c19e4224301233e9c0ea2c0e4c1b0a6c2dde53e69002d","cross_cats_sorted":["cs.DS","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-09-04T13:07:52Z","title_canon_sha256":"96e193e0dd28a1e729ae86d216fb77cd39fbff4fd4c3dfa7872ebeffe3dc8bdb"},"schema_version":"1.0","source":{"id":"1809.00932","kind":"arxiv","version":2}},"canonical_sha256":"7eed12d578a616c921192755a152944b5a964289938cf5a2e9c188bc250bee84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7eed12d578a616c921192755a152944b5a964289938cf5a2e9c188bc250bee84","first_computed_at":"2026-05-18T00:06:10.980554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:10.980554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QR2n4JJl9LOx82qau7ym9zOIAOBBUCTqbUa9pu9RsBpqY1yzwREp+jx+c7BUKqXbZPCEM3itP7amwEzn4rmZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:10.981256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00932","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4522dabc8b16f0e232a660804a412136fe0eb357420a88dfe6f156e5f36916ce","sha256:841272cc4d116806a02a97a1be02d0eb1d1f9a092efb5abf653d2b62121069ed"],"state_sha256":"bff76c03d00cc0391068b05a73623cf5318a2d6bb06fea3d44a489fb94fb38be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2MQzSccSqrBD0qKNiuZG42vTA8phTgY44XoEo2LAzcFcX8yuROAFcfySlPsrMqrn7iZ5GCOt49H8LKY2AZ6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T02:21:00.002655Z","bundle_sha256":"a4fe76f56ce7aa9372430cd78ed3668cd8b4638168adbf03adb1d1e51c249a70"}}